Stress Distribution in Peri-implant Bone in the Replacement of Molars with One or Two Implants: A Finite Element Analysis

Statement of the Problem: In most cases, insertion of single implants with a standard diameter is used to replace a molar tooth but placing two implants with a narrow diameter seems to be a viable treatment modality to withstand functional and biomechanical forces. Purpose: This study aimed to evaluate and compare stress distribution in the bone surrounding a single molar area rehabilitated by a single implant versus two implants with a narrow diameter. Materials and Method: The study was conducted by computer-aided in vitro modeling. The initial model used a single implant, 4.8 mm wide in diameter, inserted with a 3.9-mm distance from both sides and 12.6-mm mesiodistal space. The second model used two 3.3-mm narrow-sized implants with a 3-mm distance from one another, 1.5 mm from both sides, and a 12.6-mm mesiodistal space. Following the completion of these models, a 100-N force was exerted obliquely, once in three locations and once in the mesial aspect of the implant-supported crown. Stress distribution was then measured using finite element analysis (FEA) with ANSYS Workbench software package in both models. Results: The maximum stress in the bone around the single implant was less than that around double implants. The maximum stress of cortical bone in three-point loading was lower than mesial loading either in one (146.7 vs. 126.72 MPa) or two implants model (186.8 vs. 139.24). Conclusion: According to the results, because of more cortical bone contact area, the stress of surrounding bone in wide implant was decreased.


Introduction
The use of implants in full-and partial-mouth reconstructions improves masticatory function, increases patients' satisfaction, and improves their quality of life.
The mandibular first molar is the most frequent tooth replaced by implants [1]. One or two implants can be used to replace mandibular first molars. In treatment with two implants, the mesiodistal bending is limited, and both implants resist buccolingual forces [2], the risk of screw loosening decreases, the size of the cantilever reduces [3], and invasive surgeries are avoided [2].
However, there is a doubt about the quality of new bone at the graft site [4][5]. Nonetheless, in some cases, graft surgery is impossible [6]; therefore, one or two standard implants cannot be inserted, and only two narrow-diameter implants can be used. Nevertheless, the stress distribution in peri-implant bone in this treatment plan is not clear.
In the study of Desai et al. [7][8], two-splinted implant was better than single-implant in stress distribution of the bone around the implants, but in the study of de Carvalho [3], stress distribution in the bone around the single-implant was better than double-implant. Also, in the study by Hotta et al. [6], the survival rate of single-i-mplant was similar to double-implant.
The finite element analysis (FEA) is a numerical method to characterize stress and strain geometry in a three-dimensional system [1]. It is also used in dentistry to predict the distribution of stress and strain in implant components and peri-implant bone under different conditions [2]. Since increased stress in the peri-implant bone increases the odds of physiological bone resorption and failure, it is necessary to identify treatment plans that increase stress.
Considering there was a controversy among the previous studies therefore, this study compared stress distribution in peri-implant bone in replacing mandibular first molars with one standard or two narrow implants using FEA. The null hypothesis of this study was defined as in replacing mandibular first molar; the stress distribution of surrounding bone of single-and doubleimplant was similar. All the materials used in this study were considered isotropic, homogeneous, and linear elastic. The mechanical properties of the material were obtained from previous literature (Table 1) [9].  The stresses in the peri-implant bone were determined using the von Mises model [7].  (Figure 4).

Discussion
The null hypothesis of this study was rejected because the stress distribution of surrounding bone of doubleimplant was not similar to single-implant. The long-term success of implants depends on stress distribution in the surrounding bone [10]. The present study compared bone stress distribution in replacing a molar tooth with one or two implants using FEA.
In mesial loading, the stress of bone on the mesial as-   Like the present study, Desai et al. in two studies [7][8] used the FEA method to evaluate stresses in the bone around one wide implant and two implants in replacing mandibular molar. In contrast to the present study, in both studies, the Von Mises stress in the bone around a single implant was more than two implants. In addition, in a study by Gerami et al. [11], using FEA, the stress of peri-implant bone in the two-implant model was less than that around the single-implant model. In the present study in the single-implant design, due to the large diameter of the implant and the specific shape of the reconstructed mandible (the buccal depression area), the contact area with the cortical bone extended along the buccal surface of the fixture and was more widespread than in two narrow implants. Nevertheless, in the twoimplant design, the implants contacted the cortical bone only in the fixture's cervical area. Since the differences between cortical bone and titanium's elastic moduli were less than the cancellous bone, the stresses induced by a single implant to surrounding bone were lower.
Hotta et al. [6] successfully replaced one maxillary molar with two narrow implants inserted diagonally. However, they constructed mandibles with different materials from those used in this study; therefore, comparison is not possible.
In most clinical studies, replacing a molar tooth with two splinted narrow implants was successful; however, most of these studies have not compared the success rates of these two treatment plans [2,6,[14][15][16].
In a study by Wolfinger et al. [17] on 125 patients, two splinted narrow implants were used for single molar replacement in each case. At a three-year follow-up, 115 patients had two implants, but in ten patients, one implant failed, and the failed implants were not replaced.
All the single implants survived during the follow-up and one narrow implant on one side of the edentulous area survived and served as two splinted implants. It shows that despite they have a narrow diameter with a long cantilever, the peri-implant bone stress level was lower than that can be failed them.
This study's results were achieved using FEA; despite its extensive application in dentistry, it has some limitations. For instance, the bone was considered homogeneous, linearly elastic, and isotropic, 100% osseointegration was assumed; occlusal forces were considered static, and the mandibular flexure was ignored.
On the other hand, the exact simulation of clinical conditions is not possible in FEA studies, and the findings of such studies must be used with caution. For example, using two narrow splinted implants was successful in clinical studies [2, 6, 14-16] because a higher bone volume around narrow fixtures provides more perfusion and nutrition, increasing the possibility of osseointegration, which cannot be simulated in the FEA model.

Conclusion
Given the limitations of this study, in the surrounding bone of the single standard implant, the stress value was less than two splinted narrow implants, because of the unique edentulous ridge shape in the current study that increased contact area with cortical bone in the singleimplant model compared with two narrow splinted implants. Therefore, this study showed that the cortical bone-implant contact surface was more important than the total bone-implant contact surface in decreasing peri-implant bone stress level.